A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = {60^o}$. If ${B_1}$ and ${B_2}$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively, the ratio $\frac{{{B_1}}}{{{B_2}}}$ is

A straight wire of diameter $0.5\, mm$ carrying a current of $1\, A$ is replaced by another wire of $1\, mm$ diameter carrying the same current. The strength of magnetic field far away is

One metre length of wire carries a constant current. The wire is bent to form a circular loop. The magnetic field at the centre of this loop is $B$. The same is now bent to form a circular loop of smaller radius to have four turns in the loop. The magnetic field at the centre of this new loop is

A coil having $N$ $turns$ carry a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

The magnetic field at the centre of a circular current carrying-conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c$ : $B_a$ will be

Two circular coils $P$ and $Q$of $100$ turns each have same radius of $\pi \mathrm{cm}$. The currents in $\mathrm{P}$ and $\mathrm{R}$ are $1 \mathrm{~A}$ and $2 \mathrm{~A}$ respectively. $\mathrm{P}$ and $\mathrm{Q}$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{\mathrm{x}} \mathrm{mT}$, where X=___.

$\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$